The use of energy harvesting (EH) nodes as cooperative relays is an attractive solution that harnesses the spatial diversity of a multi-relay network and also addresses the vexing problem of a relay's batteries getting drained when it forwards information to the destination. For a general class of stationary and ergodic energy harvesting processes, we analytically characterize the performance of a cooperative system in which the EH nodes are amplify-and-forward relays, which volunteer to relay if and only if they have sufficient energy for transmission. We show that when such systems employ relay selection, the energy usage at any relay and, consequently, its availability for relaying depend not only on its energy harvesting process but also the total number of relays and the relay selection policy. Further insight is gained by a two-fold asymptotic analysis that considers the cases where the signal-to-noise ratio (SNR) or the number of relays is large. The optimal static transmit power setting at the EH relays is also determined. Altogether, our results show that EH relays are beneficial and different from conventional cooperative relays.